Finite Group Databasebeta

← C2×#21455926 #30548191

Subgroups — C2×#21455926 #30548191

Order 15616.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840294C211yesmaximal, characteristic, complemented
2C2×C4×#11758226C211yesmaximal, characteristic, complemented
3#21455926C2116yesmaximal, direct product factor
4C2×#16840105C211yesmaximal, characteristic, complemented
5C2×#16840084C211yesmaximal, characteristic, complemented
6C2×#16840071C211yesmaximal, characteristic, complemented
7C2×#16840065C211yesmaximal, characteristic, complemented
8C2×#16839982C211yesmaximal, characteristic, complemented
9C2×#16839976C211yesmaximal, characteristic, complemented
10C2×#16839927C211yesmaximal, characteristic, complemented
11C2×#16839906C211yesmaximal, characteristic
12C2×#16839872C211yesmaximal, characteristic, complemented
13C2×#16839867C211yesmaximal, characteristic, complemented
14C2×#16839864C211yesmaximal, characteristic, complemented
15C2×#16839817C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21#16840294—24no—
22#16840294C2218yescomplemented
23C2×#14519770—21no—
24C2×#14519768C2211yescharacteristic
25C2×#14519764C2211yescharacteristic
26C2×#14519759—21no—
27C2×#14519757C2211yescharacteristic
28C2×#14519748C2211yescharacteristic
29C4×#11758226—24no—
30C4×#11758226C2218yescomplemented
31C2×Q8×Dic61C2211yescharacteristic
32C2×C4×Dic122C2211yescharacteristic
33C2×C4×D244—21no—
34C2×C4×D244C2211yescharacteristic
35C2×#14519739—21no—
36C2×#14519739C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×#14519736—21no—
39C2×#14519735—21no—
40C2×#14519735C2211yescharacteristic
41C2×C42×D61—21no—
42C2×C42×D61C2211yescharacteristic
43#16840105C2218yescomplemented
44#16840084C2218yescomplemented
45#16840071C2218yescomplemented
46#16840065C2218yescomplemented
47#16839982C2218yescomplemented
48#16839976C2218yescomplemented
49#16839927C2218yescomplemented
50#16839906C2218yes—
51#16839872C2218yescomplemented
52#16839867C2218yescomplemented
53#16839864C2218yescomplemented
54#16839817C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758226—24no—
78C2×#11758226—24no—
79C2×#11758226—22no—
80C2×#11758226C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C2×#11758202—24no—
92C2×#11758202C2314yes—
93C2×#11758190—24no—
94C2×#11758190C2314yes—
95C2×#11758199—24no—
96C2×#11758199C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519770—28no—
100#14519768—22no—
101#14519768C2314yes—
102#14519764—22no—
103#14519764C2314yes—
104#14519759—28no—
105#14519757—22no—
106#14519757C2314yes—
107#14519748—22no—
108#14519748C2314yes—
109Q8×Dic61—22no—
110Q8×Dic61C2314yes—
111C4×Dic122—22no—
112C4×Dic122C2314yes—
113C4×D244—28no—
114C4×D244—22no—
115C4×D244C2314yes—
116#14519739—28no—
117#14519739—22no—
118#14519739C2314yes—
119C4×C22⋊D61—28no—
120#14519736—28no—
121#14519735—22no—
122#14519735—28no—
123#14519735C2314yes—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×C22⋊Dic61—21no—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144C42×D61—28no—
145C42×D61D414yes—
146C42×D61C2314yes—
147#14519711C2314yes—
148#14519708C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519702C2314yes—
153#14519701C2314yes—
154#14519700C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160#14519688C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C2×SD16×C61—24no—
165C2×SD16×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C4×D4×C61—22no—
171C4×D4×C61C2314yes—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178#107×C61C2314yes—
179#103×C61C2314yes—
180#102×C61C2314yes—
181#97×C61C2314yes—
182C24×C61—21no—
183C23×D61—21no—
184C23×D61C2×D411yescharacteristic
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61#4114yes—
188C2×Q8×C61C2412yes—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61C2412yes—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—24no—
197C22×C4×C61—44no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—44no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209#11758226—216no—
210#11758226—28no—
211#11758226—28no—
212C2×D244—28no—
213C2×D244—24no—
214C2×D244—21no—
215C2×D244—22no—
216C2×D244#4114yes—
217C2×D244C2412yes—
218C2×C4×D61—28no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—42no—
225C2×C4×D61—42no—
226C2×C4×D61—44no—
227C2×C4×D61—44no—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2×D414yes—
230C2×C4×D61C2×D414yes—
231C2×C4×D61C2412yes—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—21no—
235C2×Dic122C2412yes—
236SD16×C61—28no—
237C2×C8×C61—22no—
238C2×C8×C61—22no—
239C2×C8×C61C2412yes—
240C2×C8×C61C2412yes—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C22⋊C4×C61—24no—
247C42×C61—24no—
248C42×C61C2×D412yes—
249C42×C61C2412yes—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253#11758202—28no—
254#11758199—28no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—24no—
262C4⋊Dic61—24no—
263C4⋊Dic61—24no—
264C4⋊Dic61C2412yes—
265C4⋊Dic61C2412yes—
266#11758196—24no—
267#11758196—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61C2×D414yes—
272C4×Dic61C2×D412yes—
273C4×Dic61C2×D414yes—
274C4×Dic61C2412yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279#11758190—28no—
280C23×C61—22no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61C22×D411yescharacteristic
285C22×D61—22no—
286C22×D61—24no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61C22×D412yes—
293Q8×C61—24no—
294Q8×C61—22no—
295Q8×C61C2×#4114yes—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—42no—
299C2×C4×C61—24no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—48no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2×#4112yes—
313C2×C4×C61C2511yescharacteristic
314C22⋊D61—48no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D412yes—
326C2×Dic61C22×D412yes—
327D244—216no—
328D244—24no—
329D244—22no—
330D244C2×#4114yes—
331C4×D61—216no—
332C4×D61—24no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—44no—
336C4×D61—44no—
337C4×D61—48no—
338C4×D61—48no—
339Dic122—22no—
340Dic122—22no—
341Dic122—42no—
342C8×C61—22no—
343C8×C61—22no—
344#92418—22no—
345#92418—22no—
346C2×#3111—611nomaximal, Sylow
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—84no—
351C22×C61#52512yes—
352C22×C61#57512yes—
353C22×C61#57512yes—
354C22×C61C23×D411yescharacteristic
355C2×D61—22no—
356C2×D61—24no—
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—44no—
360C2×D61—48no—
361C2×D61—42no—
362C2×D61—42no—
363C4×C61—24no—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61#52512yes—
369C4×C61C22×#4111yescharacteristic
370C4×C61C22×#4111yescharacteristic
371Dic61—22no—
372Dic61—22no—
373Dic61—22no—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377C2×#529—611no—
378C2×C4×#41—611no—
379#3111—6116no—
380C2×#485—611no—
381C2×#482—611no—
382C2×#479—611no—
383C2×#478—611no—
384C2×#464—611no—
385C2×#463—611no—
386C2×#452—611no—
387C2×#449—611no—
388C2×#442—611no—
389C2×#441—611no—
390C2×#440—611no—
391C2×#440D6111yescharacteristic, complemented
392C2×#432—611no—
393C2×C61—82no—
394C2×C61#311114yescomplemented
395C2×C61C2×#52511yescharacteristic
396C2×C61C2×#57511yescharacteristic
397C2×C61C2×#57511yescharacteristic
398D61—42no—
399D61—44no—
400C22×#41—611no—
401C22×Q16—611no—
402C22×SD16—611no—
403C22×SD16C2×D6111yescharacteristic
404C22×D8—611no—
405#529—618no—
406#529—1224no—
407C2×#126—1221no—
408C2×#125—611no—
409C2×#124—611no—
410C2×#123—1221no—
411C2×C22⋊Q8—611no—
412C2×#121—611no—
413C4×#41—618no—
414C4×#41—1224no—
415C2×C4×Q8—611no—
416C2×C4×Q8—611no—
417C2×C4×Q8C2×D6111yescharacteristic
418C2×C4×D4—611no—
419C2×C4×D4—611no—
420C2×C4×D4—1221no—
421C2×C4×D4—1221no—
422C2×C4×D4—1221no—
423C2×C4×D4C2×D6111yescharacteristic
424C2×#117—611no—
425C2×#117—1221no—
426C2×#117—1221no—
427C22×C42—611no—
428C22×C42—1221no—
429#485—618no—
430#482—618no—
431#479—618no—
432#478—618no—
433#464—618no—
434#463—618no—
435#452—618no—
436#449—618no—
437#442—618no—
438#441—618no—
439#440—618no—
440#440C2×D6118yescomplemented
441#432—618no—
442C2×#107—611no—
443C2×#107C2×D6111yescharacteristic
444C2×#106—611no—
445C2×#106—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103C2×D6111yescharacteristic
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102C2×D6111yescharacteristic
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×#97C2×D6111yescharacteristic
460C61C2×#311111yescharacteristic, complemented, Sylow
461C2×#41—614no—
462C2×#41—1222no—
463C2×#41—1224no—
464C2×#41—1224no—
465C22×Q8—611no—
466C22×Q8C22×D6111yescharacteristic
467C22×D4—611no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4C22×D6111yescharacteristic
471C23×C4—21no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C2×Q16—614no—
479C2×Q16—1224no—
480C2×SD16—24no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16C22×D6114yes—
484C2×D8—614no—
485C2×D8—1224no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490#126—1228no—
491#125—614no—
492#125—1222no—
493#124—614no—
494#124—1222no—
495#123—1228no—
496C22⋊Q8—614no—
497C22⋊Q8—1222no—
498#121—614no—
499#121—1222no—
500C4×Q8—22no—
501C4×Q8—614no—
502C4×Q8—614no—
503C4×Q8—1222no—
504C4×Q8—1222no—
505C4×Q8C22×D6114yes—
506C4×D4—22no—
507C4×D4—614no—
508C4×D4—614no—
509C4×D4—1228no—
510C4×D4—1222no—
511C4×D4—1228no—
512C4×D4—1228no—
513C4×D4—1222no—
514C4×D4C22×D6114yes—
515#117—614no—
516#117—1228no—
517#117—1228no—
518#117—1222no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—21no—
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—611no—
541C2×C42—614no—
542C2×C42—614no—
543C2×C42—1228no—
544C2×C42—1221no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42C22×D6111yescharacteristic
548#107—614no—
549#107C22×D6114yes—
550#106—614no—
551#106—614no—
552C4⋊C8—614no—
553C4⋊C8—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#103C22×D6114yes—
558#102—614no—
559#102—614no—
560#102—614no—
561#102C22×D6114yes—
562C22⋊C8—614no—
563C22⋊C8—614no—
564#97—614no—
565#97C22×D6114yes—
566C24—21no—
567C24—611no—
568C24—1221no—
569#41—1228no—
570#41—12216no—
571#41—1228no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—612no—
575C2×Q8—1221no—
576C2×Q8—1222no—
577C2×Q8—1222no—
578C2×Q8#1175822214yes—
579C2×Q8C23×D6112yes—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—614no—
584C2×D4—612no—
585C2×D4—1224no—
586C2×D4—1228no—
587C2×D4—1224no—
588C2×D4—1221no—
589C2×D4—1222no—
590C2×D4—2444no—
591C2×D4C23×D6112yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—614no—
603C22×C4—614no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—1228no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1224no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4—2444no—
616C22×C4—2444no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620Q16—1228no—
621SD16—28no—
622SD16—1228no—
623D8—1228no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8C23×D6112yes—
631C2×C8C23×D6112yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—612no—
636C4⋊C4—612no—
637C4⋊C4—1224no—
638C4⋊C4—1224no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1224no—
644C4⋊C4C23×D6112yes—
645C4⋊C4C23×D6112yes—
646C22⋊C4—24no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C22⋊C4—1224no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C42—24no—
655C42—614no—
656C42—614no—
657C42—612no—
658C42—612no—
659C42—1224no—
660C42—1224no—
661C42—1224no—
662C42D4×D6112yes—
663C42C23×D6112yes—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—612no—
669C23—1224no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—2442no—
675C23—2442no—
676C23C2×D4×D6111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—1222no—
680Q8—1222no—
681Q8—2442no—
682Q8C2×#1175822214yes—
683D4—22no—
684D4—22no—
685D4—42no—
686D4—614no—
687D4—12216no—
688D4—1224no—
689D4—1222no—
690D4—2448no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—12216no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1224no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—2444no—
714C2×C4—2444no—
715C2×C4—2448no—
716C2×C4—2448no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4C2×D4×D6112yes—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4C2×#1175822212yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—1222no—
729C8—1222no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—1222no—
735C22—1222no—
736C22—1224no—
737C22—1222no—
738C22—2444no—
739C22—2448no—
740C22—2442no—
741C22—2442no—
742C22#1684027112yes—
743C22#1684055812yes—
744C22#1684056112yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—1222no—
752C4—1222no—
753C4—1222no—
754C4—2442no—
755C4—2442no—
756C4—2442no—
757C4#1684027112yes—
758C4C2×#41×D6111yescharacteristic
759C4C22×#1175822211yescharacteristic
760C2—82no—
761C2—2442no—
762C2—2444no—
763C2#2145592614yesdirect product factor
764C2C2×#1684027111yescharacteristic
765C2C2×#1684055811yescharacteristic
766C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#16839906C2
hypercenterC2×#440D61
hypocenterC61C2×#3111
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840294C2semidirect
2. C2×C4×#11758226C2semidirect
3. #21455926C2direct (N × H)
4. C2×#16840105C2semidirect
5. C2×#16840084C2semidirect
6. C2×#16840071C2semidirect
7. C2×#16840065C2semidirect
8. C2×#16839982C2semidirect
9. C2×#16839976C2semidirect
10. C2×#16839927C2semidirect
12. C2×#16839872C2semidirect
13. C2×#16839867C2semidirect
14. C2×#16839864C2semidirect
15. C2×#16839817C2semidirect
16. C2×C61×#440C2semidirect
22. #16840294C22semidirect
30. C4×#11758226C22semidirect
43. #16840105C22semidirect
44. #16840084C22semidirect
45. #16840071C22semidirect
46. #16840065C22semidirect
47. #16839982C22semidirect
48. #16839976C22semidirect
49. #16839927C22semidirect
51. #16839872C22semidirect
52. #16839867C22semidirect
53. #16839864C22semidirect
54. #16839817C22semidirect
72. C61×#440C22semidirect
391. C2×#440D61semidirect
394. C2×C61#3111semidirect
440. #440C2×D61semidirect
460. C61C2×#3111semidirect
763. C2#21455926direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168402942
C2×C4×#117582262
#214559262
C2×#168401052
C2×#168400842
C2×#168400712
C2×#168400652
C2×#168399822
C2×#168399762
C2×#168399272
C2×#168399062
C2×#168398722
C2×#168398672
C2×#168398642
C2×#168398172
C2×C61×#4402
C2×#311161